The on-line heilbronn’s triangle problem in d dimensions

Authors:
Gill Barequet;Alina Shaikhet
Affiliations:
Dept. of Computer Science, Technion—Israel Institute of Technology, Haifa, Israel;Dept. of Computer Science, Technion—Israel Institute of Technology, Haifa, Israel
Venue:
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Year:
2006

Citing 4
Cited 1

A Lower Bound for Heilbronn's Triangle Problem in d Dimensions

SIAM Journal on Discrete Mathematics
The average-case area of Heilbronn-type triangles

Random Structures & Algorithms
On Heilbronn’s Problem in Higher Dimension

Combinatorica
Distributions of points in d dimensions and large k-point simplices

COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics

Heilbronn's triangle problem

SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry

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Abstract

In this paper we show a lower bound for the on-line version of Heilbronn’s triangle problem in d dimensions. Specifically, we provide an incremental construction for positioning n points in the d-dimensional unit cube, for which every simplex defined by d + 1 of these points has volume Ω(1/n$^{\rm ({\it d}+1)ln ({\it d}--2)+2}$).